Complexities of normal bases constructed from Gauss periods

DOI10.1007/S10623-017-0368-YzbMath1414.11163OpenAlexW2619722410MaRDI QIDQ1741928

Xiang-Dong Hou

Publication date: 10 April 2018

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-017-0368-y

zbMATH Keywords

finite fieldnormal basisGauss periodcyclotomic number

Mathematics Subject Classification ID

Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Cyclotomy (11T22) Solving polynomial systems; resultants (13P15)

Cites Work

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• Gauss periods as constructions of low complexity normal bases
• Optimal normal bases in \(GF(p^ n)\)
• Algorithms for exponentiation in finite fields
• Complete solution of the cyclotomic problem in $F_q$ for any prime modulus $l, q = p^α, p ≡ 1 (mod l)$
• Jacobi sums and cyclotomic numbers of order l²
• The cyclotomic numbers of order twelve
• Cyclotomic numbers of order 2l, l an odd prime
• Cyclotomy, Higher Congruences, and Waring's Problem
• The cyclotomic numbers of order fourteen
• The Cyclotomic Numbers of Order Eighteen with Applications to Difference Sets

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